From Wide Angle Reflection To Leaking Mode Seismograms - A Theoretical And Experimental Study

Abstract

Seismograms observed by a detector in the wide angle reflection to leaking mode region, (the intermediate zone), exhibit a plethora of interesting features. Head waves form and interfere with directly reflected arrivals, supercritically reflected waves have unusually large amplitudes and the normal and leaking modes gradually become predominant with increasing source- receiver separation. This transition region from seismograms consisting mostly of directly reflected waves to seismograms where the total characteristics of the medium are integrated by the normal and leaking modes in therefore an important area of study. The eigenfunction expansion of an infinite medium elastic wave field in Cartesian co-ordinators is an infinite series of plane waves describing generalized rays with real and complex angles of propagation. The expansion can be modified for a place layered medium by assigning transmission factors to the rays at they encounter each interface producing further rays. The “Sherwood-Cagniard” technique, (Sherwood (1958 and 1960)), provides a methods of evaluating the eigenfunction solution for an impulsive line source. In this thesis it has been used in a modified form to give closed solution for rays which follow and ascribed sequence of transmissions and velocities in a two dimensional medium. Furthermore, this solution is shown to be easily related to cylindrically symmetric three dimensional wave propagation. The mathematical method is ideally suited to generating synthetic seismograms in the intermediate zone. The technique is developed and made systematic by a ray indexing methods for computer programming purposed. Theoretical seismograms thus computed are then compared with experimental seismograms observed on models. The transmission factor assigned to rays with a given angle of propagation are functions only of the angle between the rays’ wave-front and the interface. Thus the method is extended to plane dipping interfaces and the theoretical seismograms compared with experiment. Finally an attempt is made to generalize the technique to curved interfaces. Even here some agreement is obtained with the experimental seismograms. The experimental seismograms are measured on a calibrated two dimensional seismic model system. The system features a new construction technique with bongs glass to epoxy to form layer over a half space models with curved, dipping or horizontal interfaces.